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Nori motives of curves with modulus and Laumon 1-motives

Florian Ivorra and Takao Yamazaki

Let k be a number field. We describe the category of Laumon 1-isomotives over k as the universal category in the sense of Nori associated with a quiver representation built out of smooth proper k-curves with two disjoint effective divisors and a notion of $H^1_\dR$ for such "curves with modulus". This result extends and relies on the theorem of J. Ayoub and L. Barbieri-Viale that describes Deligne's category of 1-isomotives in terms of Nori's Abelian category of motives.

Reference : Canadian Journal of Mathematics , Volume 70 , Issue 4 , 01 August 2018 , pp. 868 - 897 https://doi.org/10.4153/CJM-2017-037-x

ArXiv link : https://arxiv.org/abs/1609.08279

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